Now we transition into the entirely new framework of Lagrangian mechanics. The purpose of this formulation is to cast the elements of classical mechanics into a much more general, rigorous, and beautiful form. We will introduce a new object called the Lagrangian ($L$), and show how it can provide us with all the familiar results of Newtonian mechanics. We will then derive the Euler-Lagrange equation, which is the equation of motion in this framework (analogous to Newton’s second law). Lastly, we will delve deeper into the nature of the universe by discussing the powerful connection between conservation laws and symmetries.